The Ludi Romani were Roman public games honoring Jupiter Optimus Maximus that were celebrated from the 5th century B.C. Before 220 B.C., they were limited to one day, the Ides of September, but by A.D. 51, funding (760,000 sesterces) was provided for 14 days ["Appropriations for the Games at Rome in 51 A.D.," by William M. Green. The American Journal of Philology, Vol. 51, No. 3 (1930), pp. 249-250]. Curule aediles were in charge of the Ludi Romani.
The Ludi Romani included a procession from the Capitol to the Circus Maximus that was followed by a sacrifice, feasts to Jupiter and then both theatrical productions and chariot races (games).
For the connection between the Ludi Romani, triumphs, and events ushering in the new year, see this review (or the book reviewed): "Review: The Triumph," by R. M. Ogilvie;The Classical Review, New Series, Vol. 23, No. 1 (Mar., 1973), pp. 75-77.